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Half Independence and half cumulants

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Half Independence and half cumulants
2.	Creator	Author's name, affiliation, country	Arup Bose; Indian statistical institute, Kolkata
2.	Creator	Author's name, affiliation, country	Rajat Subhra Hazra; Indian statistical institute, Kolkata
2.	Creator	Author's name, affiliation, country	Koushik Saha; Bidhannagar Government College, Kolkata
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Cramer's theorem; Central limit theorem; cumulant; $C^*$probability space; free algebras; free independence; half commutativity; half independence; noncommutative probability spaces; reverse circulant matrix; Rayleigh distribution; semicircular law;
3.	Subject	Subject classification	60B20; 46L53; 46L54; 60B10
4.	Description	Abstract	The notion of half independence arises in random matrices and quantum groups. This notion is available only for elements of a noncommutative probability space and assumes the existence of all moments. We relate half independence to a certain class of partitions and use it to define an appropriate cumulant generating function and a transform which is closely related to the characteristic function. This leads to a definition of half independent convolution of arbitrary probability measures which is compatible with the distribution of the sum of half independent elements of a noncommutative probability space. We also establish the central limit theorem for half independent convolution of measures with the limit being symmetrized Rayleigh. Cramer's theorem is also established in this set up.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	J.C.Bose Fellowship, Government of India
7.	Date	(YYYY-MM-DD)	2011-04-08
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1651
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1651
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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